Byron amended the roof membrane repair work costs from $120,000 to $180,000 during a meeting on Wednesday night.

In arguing for the first time that the proposed $2.1 million plan is too costly, Byron said engineers had begun Tuesday to examine covering the leaky roof with a membrane that might last for several years. School board members discussed the idea briefly at a meeting last week.

“I don’t think we can afford to invest a few million in the roof, but we can put a new membrane on it,” Byron said Tuesday night. “I will be talking about it with the architect. It will probably take a few weeks to see if it is a viable option.”

The idea might end the controversial debate in this northern Penobscot County community over the roof repair proposal — and, by extension, the future of the high and elementary schools underneath it.

The $2.1 million proposal calls for new R-38 roof insulation, a new gymnasium floor, emergency and exit lights, audio-visual fire alarms, repairing gym wall cracks, and remodeling bathrooms and drinking fountains to meet Americans With Disabilities Act requirements. The state would pay about $636,000 of the total.

The work is expected to raise the town’s 23.33 mill rate at least 1.1 mills — or $54 in property tax annually on property worth $50,000. The building serves about 280 students from East Millinocket, Medway and Woodville, including Opal Myrick Elementary School, which moved into a wing in 2011.

But the town faces declining school-age and general populations, rising education costs, and shrinking state aid and local tax bases within a Katahdin region economy that typically has an unemployment rate that runs double the state average.

Estimates place the school population decline at 55 percent since 1995.

A board vote on Tuesday on whether to support the $2.1 million repair project deadlocked in a 2-2 tie. Byron and Jennifer Murray voted against it; Angel Danforth and Ryan Whitehouse voted for it. Mark Wallace was absent. Byron said the board will vote re-vote when Wallace is present.

Tuesday’s school board meeting was easily the most contentious regarding the roof work. In letters submitted to the board, the East Millinocket and Medway teachers’ unions announced no-confidence votes in Murray and called for her resignation.

The Medway union’s letter accused Murray of “negativity” and creating “negative publicity.” The East Millinocket letter said that Murray “does not have the best interests of the physical school building and even of having a school in the town of East Millinocket in the future.”

“She, along with the selectmen, have blocked the democratic process in the town by delaying a public hearing and a [referendum] vote,” the letter continued.

The AOS 66 board seemed to immediately reject the resignation call. Murray’s only comment Wednesday was that she had no plans to resign.